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  2. Exponentiation - Wikipedia

    en.wikipedia.org/wiki/Exponentiation

    When an exponent is a positive integer, that exponent indicates how many copies of the base are multiplied together. For example, 3 5 = 3 · 3 · 3 · 3 · 3 = 243. The base 3 appears 5 times in the multiplication, because the exponent is 5. Here, 243 is the 5th power of 3, or 3 raised to the 5th power.

  3. Like terms - Wikipedia

    en.wikipedia.org/wiki/Like_terms

    In mathematics, like terms are summands in a sum that differ only by a numerical factor. [1] Like terms can be regrouped by adding their coefficients. Typically, in a polynomial expression, like terms are those that contain the same variables to the same powers, possibly with different coefficients.

  4. Sums of powers - Wikipedia

    en.wikipedia.org/wiki/Sums_of_powers

    In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.

  5. Order of operations - Wikipedia

    en.wikipedia.org/wiki/Order_of_operations

    When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication and placed as a superscript to the right of their base. [2] Thus 3 + 5 2 = 28 and 3 × 5 2 = 75. These conventions exist to avoid notational ambiguity while allowing notation to remain brief. [4]

  6. Van der Corput's method - Wikipedia

    en.wikipedia.org/wiki/Van_der_Corput's_method

    The method of exponent pairs gives a class of estimates for functions with a particular smoothness property. Fix parameters N , R , T , s ,δ. We consider functions f defined on an interval [ N ,2 N ] which are R times continuously differentiable , satisfying

  7. Floating-point arithmetic - Wikipedia

    en.wikipedia.org/wiki/Floating-point_arithmetic

    A simple method to add floating-point numbers is to first represent them with the same exponent. In the example below, the second number (with the smaller exponent) is shifted right by three digits, and one then proceeds with the usual addition method: 123456.7 = 1.234567 × 10^5 101.7654 = 1.017654 × 10^2 = 0.001017654 × 10^5

  8. Ordinal arithmetic - Wikipedia

    en.wikipedia.org/wiki/Ordinal_arithmetic

    The definition of exponentiation can also be given by transfinite recursion on the exponent β. When the exponent β = 0, ordinary exponentiation gives α 0 = 1 for any α. For β > 0, the value of α β is the smallest ordinal greater than or equal to α δ · α for all δ < β. Writing the successor and limit ordinals cases separately: α 0 = 1.

  9. Associative property - Wikipedia

    en.wikipedia.org/wiki/Associative_property

    If a binary operation is associative, repeated application of the operation produces the same result regardless of how valid pairs of parentheses are inserted in the expression. [2] This is called the generalized associative law. The number of possible bracketings is just the Catalan number, , for n operations on n+1 values.